Question

Determine o conjunto verdade da inequação: -2x-8/-x+2≤0

Answer 1

(-2x-8)/(-x+2) ≤0

++++++++++++++++++++++++++++++++++++++++++

y=ax+b

Se a < 0 +++++++++++++++++++++++++(raiz)--------------------------------

Se a > 0 -----------------------------------------(raiz)+++++++++++++++++++++++

q=-2x-8    ==>raiz    -2x-8=0 ==> -2x=8  ==>x=-4

a=-2<0

q++++++++++++++++++++++++++++(-4)----------------------------------------

p= -x+2  ==>raiz    -x+2=0  ==> -x=-2 ==> x=2

a=-1<0

p++++++++++++++++++++++++++++++(2)-----------------------------------------

Estudo de sinais:

q+++++++++++++(-4)---------------------------------------

p++++++++++++++++++++++++++(2)------------------

q/p+++++++++++(-4)------------------(2)++++++++++++

queremos ≤ 0  , Observe que p ≠ 2 , é o denominador

[-4 , 2)   é a resposta

Answer 2

$\frac{ - 2x - 8}{ - x + 2} \leqslant 0 \\ \\ - 2x - 8 \leqslant 0 \\ - x + 2 > 0 \\ \\ - 2x - 8 \geqslant 0 \\ - x + 2 < 0 \\ \\ x \geqslant - 4 \\ x < 2 \\ \\ x \leqslant 4 \\ x > 2 \\ \\ xe - 4 \: \: 2$